A question about uniqueness of initial conditions

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SUMMARY

The discussion centers on the uniqueness of initial conditions in second-order linear differential equations. Participants clarify that the uniqueness theorem ensures that a solution to such equations is uniquely determined by its initial conditions. The conversation references a previous thread titled "a property of differential equations" for further context. The emphasis is on understanding that the uniqueness of the solution is directly tied to the uniqueness of the initial conditions provided.

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  • Study the uniqueness theorem for second-order linear differential equations
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Hİ. How can we sure that the initial conditions , say, for a second-order linear equation must be unique which is also the uniqueness of the solution.
 
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I think I just answered this in the thread "a property of differential equations" so I won't repeat all. Please read that.

However, I'm not sure what you mean by "the initial conditions must be unique". Are you simply referring to the uniqueness of the solution satisfying initial conditions.
 
HallsofIvy said:
I think I just answered this in the thread "a property of differential equations" so I won't repeat all. Please read that.

However, I'm not sure what you mean by "the initial conditions must be unique". Are you simply referring to the uniqueness of the solution satisfying initial conditions.

Yes, it is about uniqueness theorem from the initial conditions viewpoint.
 

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